Sen. Mitch McConnell discusses how he would run the Senate if he becomes majority leader

Toward the end of a speech at a conservative think tank laying out his vision for a Republican-led Senate in 2015, Kentucky Sen. Mitch McConnell apologized Thursday for going deep into the parliamentary weeds.

"I hope you're not bored by a discussion of process," he said. "But process is important. How you deal with something has a heck of a lot to do with what kind of outcome you get."

It was the latest signal that McConnell as much as anyone is aware of the possible conundrum he'd face if he replaces Nevada Democrat Harry Reid as Senate majority leader: Republicans might win a thin majority this fall, but agreeing on what to do with it won't be easy -- particularly when his side includes staunch conservatives, institutionalists and moderates with different political pressures.

So as McConnell works toward the job he's always wanted, he's preparing to work with the hand he's been dealt. His approach? When you don't agree on policy, at least agree on process.

"We won't all agree, of course, on the particulars of every single proposal," he said. "But that's OK. The idea isn't to agree on everything. It's to have a serious debate that leads to good, durable results."

It's an idea that's resonating with other key Republicans. Sen. Ted Cruz (R-Texas), who has criticized the GOP's congressional leadership in the past for not standing strongly enough for conservative proposals, said opening up the process is critical.

"I emphatically agree that with Republicans in the majority we will begin to have substantive debates on what the American people want us talking about," he said in a recent interview. "Not everyone will agree on every issue. But having those debates, having those votes ... that's what we're supposed to be doing. And under the Harry Reid do-nothing Senate we don't do any of it."

Days after defeating his tea party challenger and winning support from some of the same conservative groups that had spent money to defeat him, McConnell used the Thursday morning speech at the conservative American Enterprise Institute to expand on a January address in which he laid out how he would run the Senate.

He promised to "break sharply from the practices of the Reid era," renewing a robust amendment process and empowering committees to restore the Senate to its role as a moderating institution.

McConnell also pledged a more "free-wheeling approach" if he becomes majority leader next year.

Notably, he said he would protect the current 60-vote threshold for advancing legislation and said Republicans would discuss whether to reverse the Democrats' filibuster-rule change that allowed most presidential nominees to advance with a simple majority vote.

He claimed that Reid's effective "gag rule" on allowing amendments has hurt Democrats as much as Republicans, and said Reid had taken to running the institution with a stronger hand than even the "tyrannical" Lyndon Johnson had when he was majority leader.

"After castigating Sen. Reid for crowding out the rest of us and shielding his actions from public view, I assure you we're not going to turn around and do the same thing," McConnell said. "There's not a chance."

A Reid spokesman scoffed at McConnell's remarks, noting that the Kentucky Republican had once declared himself the "proud guardian of gridlock."

"Senator McConnell's desperate plea of, ‘this time I'll change, I swear,' is belied by his long record as the leading force for gridlock and obstruction in Washington," said the spokesman, Adam Jentleson.